On a variant of Pillai’s problem

Kwok Chi Chim, István Pink, Volker Ziegler

Type: Article

Publication Date: 2017-02-01

Citations: 23

DOI: https://doi.org/10.1142/s1793042117500981

Abstract

In this paper, we find all integers $c$ having at least two representations as a difference between a Fibonacci number and a Tribonacci number.

Locations

International Journal of Number Theory - View
arXiv (Cornell University) - View - PDF
DEA (University of Debrecen) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	On a problem of Pillai with Fibonacci numbers and powers of 2	2017	Mahadi Ddamulira Florian Luca Mihaja Rakotomalala
+	On the problem of Pillai with Tribonacci numbers and powers of 3	2019	Mahadi Ddamulira
+	On a problem of Pillai with Fibonacci numbers and powers of $3$	2019	Mahadi Ddamulira
+	On the problem of Pillai with Fibonacci numbers, Padovan numbers, and Tribonacci numbers and powers of $3$	2019	Mahadi Ddamulira
+	On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3	2020	Mahadi Ddamulira Florian Luca
+	A Pillai-Catalan-type problem involving Fibonacci numbers	2024	Seyran S. Ibrahimov Nazım I. Mahmudov
+	On a variant of Pillai problem: integers as difference between generalized Pell numbers and perfect powers	2022	Jonathan García Carlos A. Gómez
+ PDF Chat	On Pillai's problem with Pell numbers and powers of 2	2019	Mohand Ouamar Hernane Florian Luca Salah Eddine Rihane Alain Togbé
+	ON PILLAI'S PROBLEM WITH TRIBONACCI NUMBERS AND POWERS OF 2	2017	Jhon J. Bravo Florian Luca Karina Yazan
+ PDF Chat	On a problem of Pillai with k–generalized Fibonacci numbers and powers of 2	2018	Mahadi Ddamulira Carlos A. Gómez Florian Luca
+ PDF Chat	On the problem of Pillai with Tribonacci numbers and powers of $3$	2019	Mahadi Ddamulira
+ PDF Chat	On the Pillai's problem involving two linear recurrent sequences: Padovan and Fibonacci	2022	Pagdame Tiebekabe Serge Adonsou
+ PDF Chat	On a variant of Pillai’s problem involving S-units and Fibonacci numbers	2022	Volker Ziegler
+	On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime	2022	Herbert Batte Mahadi Ddamulira Juma Kasozi Florian Luca
+	A Pillai-type problem involving Fibonacci numbers	2024	Seyran S. Ibrahimov Nazım I. Mahmudov
+	A PROBLEM ON PALINDROMIC NUMBERS	1997	Koji Yamashita
+	An analogue of Eminian’s problem for the Fibonacci number system	2022	А. А. Жукова А. В. Шутов
+	A VARIANT OF THE CONGRUENT NUMBER PROBLEM	2024	Jerome T. Dimabayao Soma Purkait
+	On Pillai’s problem with the Fibonacci and Pell sequences	2018	Santos Hernández Hernández Florian Luca Luis Manuel Rivera
+ PDF Chat	On a problem of Pillai with Fibonacci numbers and powers of 3	2019	Mahadi Ddamulira

Works That Cite This (23)

Action	Title	Year	Authors
+	On a variant of Pillai's problem II	2017	Kwok Chi Chim István Pink Volker Ziegler
+	A Hasse-type principle for exponential Diophantine equations over number fields and its applications	2018	Csanád Bertók Lajos Hajdu
+ PDF Chat	On a problem of Pillai with k–generalized Fibonacci numbers and powers of 2	2018	Mahadi Ddamulira Carlos A. Gómez Florian Luca
+	On a variant of Pillai problem: integers as difference between generalized Pell numbers and perfect powers	2022	Jonathan García Carlos A. Gómez
+	On Pillai’s problem with the Fibonacci and Pell sequences	2018	Santos Hernández Hernández Florian Luca Luis Manuel Rivera
+ PDF Chat	Integers representable as differences of linear recurrence sequences	2021	Robert F. Tichy Ingrid Vukusic Daodao Yang Volker Ziegler
+	On the problem of Pillai with Padovan numbers and powers of 3	2019	Mahadi Ddamulira
+ PDF Chat	On Pillai's problem with Pell numbers and powers of 2	2019	Mohand Ouamar Hernane Florian Luca Salah Eddine Rihane Alain Togbé
+ PDF Chat	Pillai's problem with Padovan numbers and powers of two	2019	Ana María García Lomeli Santos Hernández Hernández
+	On the Diophantine equation 𝑈_{𝑛}-𝑏^{𝑚}=𝑐	2023	Sebastian Heintze Robert F. Tichy Ingrid Vukusic Volker Ziegler

Works Cited by This (22)

Action	Title	Year	Authors
+	A new approach to Baker's theorem on linear forms in logarithms III	1988	Gisbert Wüstholz
+	A new approach to Baker's theorem on linear forms in logarithms I	1987	Gisbert Wüstholz
+	Logarithmic forms and group varieties.	1993	A. Baker Gisbert Wüstholz
+	A generalization of a theorem of Baker and Davenport	1998	Andrej Dujella Attila Pethö
+	Primary cyclotomic units and a proof of Catalans conjecture	2004	Preda Mihăilescu
+	An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers	1998	E M Matveev
+	Powers of Two in Generalized Fibonacci Sequences	2012	Jhon J. Bravo Florian Luca
+	Linear forms in the logarithms of algebraic numbers	1966	A. Baker
+ PDF Chat	THE EQUATIONS 3<i>x</i><sup>2</sup>−2 = <i>y</i><sup>2</sup> AND 8<i>x</i><sup>2</sup>−7 = <i>z</i><sup>2</sup>	1969	A. Baker H. Davenport
+	Algebraische Punkte auf Analytischen Untergruppen algebraischer Gruppen	1989	Gisbert Wüstholz